Is there a mechanism deficit in ecology?

INTECOL 2013

Agenda

Macroecology is mechanism-less? Mechanism in ecology Mechanism in physics Example 1 – distribution &

abundance Example 2 - biogeography

Macroecology – a mechanism deficit?

“If you can do a regression and pull data out of a journal you can do macroecology”

MachineLearning

p<0.05 I did science!?

Agenda

Macroecology is mechanism-less? Mechanism in ecology Mechanism in physics Example 1 – distribution &

abundance Example 2 - biogeography

Reductionism

Sadava et al

Causality

Biology is hierarchical reified

Causality moves up

Mechanism comes from below

Ricklefs

Potochkin & McGill 2012

Generalized Lotka Volterra

[𝑎1 1 ⋯ 𝑎1𝑆

⋮ ⋱ ⋮𝑎𝑆 1 … 𝑎𝑆𝑆 ]

-2 0 2 40

2000

4000

0.2

Navg

log10

(N)

(A)

0 5 100

5000

10000 0.9

CV of N(B)

0 0.5 10

500

10000.1

Nmin

vs. Nmax

(C)

0 0.5 10

500

10000.2

Nmin

vs. top 5 N(D)

0 0.5 10

500

1000

0.3

Bottom 5 N vs top 5 N(E)

0 0.5 10

500

1000

0.4

% Nt<(top 5 N)/2(F)

But does it work?

1970 1990 20100

10

20

30

Year

Nt

(A)

1970 1990 20100

10

20

30

Year

Nt

(B)

1970 1990 20100

50

100

Year

Nt

(C)

1970 1990 20100

200

400

600

Year

Nt

(D)

1970 1990 2010200

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400

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Year

Nt

(E)

1970 1990 20100

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20

30

Year

Nt

(F)

1970 1990 20100

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20

Year

Nt

(G)

1970 1990 20100

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40

Year

Nt

(H)

1970 1990 20100

1

2

Year

Nt

(I)-2 0 2 40

2000

4000

0.2

Navg

log10

(N)

(A)

0 5 100

5000

10000 0.9

CV of N(B)

0 0.5 10

500

10000.1

Nmin

vs. Nmax

(C)

0 0.5 10

500

10000.2

Nmin

vs. top 5 N(D)

0 0.5 10

500

1000

0.3

Bottom 5 N vs top 5 N(E)

0 0.5 10

500

1000

0.4

% Nt<(top 5 N)/2(F)

0 20 400

1

2

3

Nt

t

(A)

0 20 40 600

1

2

3

Nt

t

(B)

0 10 200

1

2

3

Nt

t

(C)

0 50 1000

1

2

3

Nt

t

(D)

0 200 400 6000

1

2

3

Nt

t

(E)

0 0.5 10

500

1000

0.3

r2(F)

McGill 2013 (in The Balance of Nature and Human Impact ed. Rohde)

The equilibrial target is always moving!

27.20%

16.20%

16.40%22.70%

17.50%

Frequency HorizontalLinear sloping upLinear sloping downQuadratic convex upQuadratic convex down

Agenda

Macroecology is mechanism-less? Mechanism in ecology Mechanism in physics Example 1 – distribution &

abundance Example 2 - biogeography

Physics 1687

Newton:1. F=Ma2. F=GM1M2/d2

3. Inertia & equal/opposite reactions Descartes clockwork universe

Physics 2013

Quantum mechanics

Statistical mechanics

Mechanism in physics Practical

If you have an equation that is useful/predictive you have a mechanism (or maybe you’re just done and don’t care about mechanism?)

Laddered Quantum mechanics gives Bohr atom Physical chemistry gives multi-atom systems Ideal gas law/statistical mechanics gives relation of macro-

properties Statistical

Quantum mechanics Statistical mechanics (avoids intermediate numbers

problem) As general as possible Only occasionally reductionist (more often self-

contained) Context aware (external forcing, environment)

Conclusion Macroecology

Doesn’t have a mechanism deficit Has a mechanism recognition deficit

Mechanisms in ecology: AWOL or Purloined Letter. Towards a practical view of mechanism. 2010 McGill & Nekola

Agenda

Macroecology is mechanism-less? Mechanism in ecology Mechanism in physics Example 1 – distribution &

abundance Example 2 - biogeography

A thought experiment – sampling from the region

Region

Small localcommunityN=2, S=2

Larger localcommunityN=4, S=3

We can write sampling idea as equations

S, N, Ni, A from region are inputsPivotal idea is sampling function:

P=(ni|Ni,a,A,)

McGill 2011 American Journal Botany

Also see:Etienne & Alonso 2005Green & Plotkin 2007He & Legendre 2002Dewdney 1998Pielou multiple

How are we doing?

Surprisingly not too bad, but we’re missing something (too much , not enough )

0 10 20 30 40 5050

100

150

200

250

Area (ha)

S

(A)

Actual Ni

All equal Ni=N*/S

Actual SAR

60 80 100 120 1400

5

10

15

Observed=90.78

Sampled=103.94

Equal N=78.4

Local ( α) richness s

no. s

ites

(B)

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

Actual Oi

Pred

icte

d (ran

dom

)O

i

(C)

0 0.2 0.4 0.6 0.8 10

100

200

300

400

Observed=0.67

Sampled=0.92

Need another assumption Have been using sampling

function, , as spatially random (binomial or Poisson form)

We know clumped in nature Clumping would fix

problems (reduce , increase )

More individuals from same species in sample lowers

More individuals from same species in one sample, likely to be underrepresented in other sample increases

Condit et al 2000

Clumping fixes it!

=Finite Negative Binomial (Zillio & He 2010)

0 20 40 6050

100

150

200

250

Area (ha)

# S

peci

es

ActualBinomialAgg Binom

60 80 100 1200

5

10

1590.04 91.00

α diversity

# co

mm

uniti

es0 0.5 1

0

0.5

1

Actual Oi

Agg

Bin

Pre

d O

i

Sampling works at small scales

Scale-break100km X 100km

Deterministic absencesMoving out of range

Stochastic absencesSampling

Spatially explicit, larger scale version

WIDTH

WIDTH

A

B

mi

RADIUSi

EXTENT

Abundance

Spatial extent

MVPi

Range Boundary

si

mi

Ni(X)=NMAXi exp(||X- mi||2/s2)

X

McGill & Collins 2003Also seeGauch & Whittaker 1972Allen & White 2003

3 assumptions common to many theories

3 Assumptions1. Species

abundance varies logarithmically

2. Individuals in 1 species are clumped

3. All else can be random

McGill Ecology Letters 2010

Agenda

Macroecology is mechanism-less? Mechanism in ecology Mechanism in physics Example 1 – distribution &

abundance Example 2 - biogeography

Back to Leibig’s Law?Gause Leibig biogeographic law

Any one variable sets an upper limit according to a Gause’s law (Gaussian bell-curve)

But most sites at the optimum are limited by something else

It appears to be very general

It appears very general

Bruce Martin Wikimedia under CCA

In the lab can home in on limiting factor

CristianSolari

Environment and Organisms What

Dozens of GIS layers of climate that are biologically relevant for use in distribution modelling

Bioagricultural (e.g. degree days, frost free days, drought)

Extreme events (10-year coldest day, 50 year drought)

Topographic (slope, aspect, moisture indices)

Landcover Traditional climate

Publically served, global 1km co-registered Status

Funding from 3 organizations, >30 people involved

Pieces starting to become publically available

Non-stationarity is now helpful

80 W 90

W

Predicted

100 W 110

W

25 N

35 N

45 N

50 N

30 N

40 N

10

20

30

40

50

60

clDD

clPclTmean

clTmax

clTmin

ndvisePsd

seTrn

Can dopredictions

10-1

100

101

102

103

10-1

100

101

102

Actual

Pre

dict

ed

10-1

100

101

102

103

100

101

102

Actual

Pre

dict

ed

r2 limit=0.47321 r2 tree=0.32954; RMSE limit=25.1077, RMSE tree=26.2827

Summary Mechanism is not deterministic

and reductionist Mechanism is often stochastic, self-

referential, context-sensitive, more general than biology

Macroecology already has many mechanisms! Sampling w/ clumping Gause’s normal curve & Liebig’s Law